Question

The time period of a freely suspended magnet is 4 seconds. If it is broken in length into two equal parts and one part is suspended in the same way, then its time period will be
\[\begin{align}
  & A)4s \\
 & B)2s \\
 & C)0.5s \\
 & D)0.25s \\
\end{align}\]

Answer 1

Hint: Here, a magnet is cut into two equal halves. The initial time period of the magnet is given in the question. To calculate the new time period of a magnet, we have an equation which relates the number of cuts and the original time period of the magnet. Substitute the values given in the equation to find out the new time period of the suspended magnet.
Formula used:
\[T=nT'\]
\[T=2\pi \sqrt{\dfrac{I}{MB}}\]

Complete step by step solution:
Given,
Initial time period of a freely suspended magnet, \[T=4s\]
Number of cuts, \[n=2\]
We have,
Time period of magnet, \[T=2\pi \sqrt{\dfrac{I}{MB}}\]
Where,
is the moment of inertia
is the magnetic moment
is the horizontal component of earth’s magnetic field
From the above equation,
\[T'=\dfrac{T}{n}\]
Where,
\[T'\] is the new time period
\[T\]is the original time period of the magnet
\[n\]is the number of cuts
Then, substitute the given values in the above equation, we get,
\[T'=\dfrac{4}{2}=2s\]

Therefore, the answer is option B.

Note:
When a bar magnet is suspended freely, it points in the north-south direction. The side which points to the geographic north is called the north Pole and the side which points to the geographic south is called the south pole of the magnet. A magnet has two poles similar to the negative and positive charge of an electric dipole. Unlike the electric field dipole, the magnetic field lines of a magnet form continuous and closed loops. In the case of an electric dipole, field lines begin from the positive charge and end either on the negative charge or escape to infinity. The magnetic field lines never intersect each other, if they did, the direction of the magnetic field would not be unique at that particular point of intersection.